Results from first-principles calculations present a rather clear picture of the interaction of SO2 with unreduced and partially reduced (111) and (110) surfaces of ceria. The Ce3+/Ce4+ redox couple, together with many oxidation states of S, give rise to a multitude of SOx species, with oxidation states from +III to +VI. SO2 adsorbs either as a molecule or attaches via its S-atom to one or two surface oxygens to form sulfite (SO32−) and sulfate (SO42−) species, forming new S–O bonds but never any S–Ce bonds. Molecular adsorption is found on the (111) surface. SO32− structures are found on both the (111) and (110) surfaces of both stoichiometric and partially reduced ceria. SO42− structures are observed on the (110) surface together with the formation of two reduced Ce3+ surface cations. SO2 can also partially heal the ceria oxygen vacancies by weakening a S–O bond, when significant electron transfer from the surface (Ce4f) into the lowest unoccupied molecular orbital of the SO2 adsorbate takes place and oxidizes the surface Ce3+ cations. Furthermore, we propose a mechanism that could lead to monodentate sulfate formation at the (111) surface.